The actress was pronounced dead three days after she suffered a fall during a beginner’s skiing lesson in the Canadian resort of Mont Tremblant.

She declined medical treatment at the scene and laughed off the incident, but later reported feeling unwell and an ambulance was called to her hotel. Her condition swiftly deteriorated and she was transferred from a local hospital to a larger unit in Montreal, where doctors established that she was brain dead. She was then flown to New York, where the family gathered to say a last goodbye.

Miss Richardson leaves two sons: Micheal, 13, and Daniel, 12. Micheal was holidaying with his mother in Mont Tremblant and accompanied her to hospital.

An autopsy report found that Miss Richardson died from an epidural haematoma – bleeding on the brain – caused by a “blunt injury to the head”.

The New York medical examiner’s office concluded that the death was an accident.

Tributes have poured in for the actress, who appeared in a string of Hollywood films but was best known for her stage work, including a Tony Award-winning performance in Sam Mendes’ Broadway revival of Cabaret.

Mr Mendes said in a statement: “It defies belief that this gifted, brave, tenacious, wonderful woman is gone. She was one of a kind, a magnificent actress. She was also an amazing mother, a loyal friend, and the greatest and most generous host you could ever hope to meet.”

Former co-star Dame Judi Dench spoke of Miss Richardson’s “incredibly luminous quality” and praised her as a “really great actress” whose best work was probably still to come.

Film star Jane Fonda, a friend of Vanessa Redgrave, wrote on her blog: “It is hard to even imagine what it must be like for her family. My heart is heavy.”